(Very)
Fast estimation and testing of (very) large dimensional heavy-tailed
elliptical distributions
David Veredas (Université
libre
de
Bruxelles)
28/01/11
We
estimate the parameters of an elliptical distribution by means of a
multivariate extension of the Method of Simulated Quantiles (MSQ) of
Dominicy and Veredas (2010). The multivariate extension entails
the construction of a function of quantiles that is informative about
the codispersion parameters: the interquantile range of a projection of
pairwise random variables onto the 45 degree line. Moreover, due
to the properties of the elliptical distributions we circumvent the
curse of dimensionality as we provide a very fast methodology
to estimate the parameters of any dimension. We also provide a
quantile-based criterion to choose the elliptical distribution. A Monte
Carlo study to 20, 200 and 2000 dimensions reveals good finite
sample properties of the estimators. Two empirical applications to 22
worldwide financial market returns and 490 asset returns illustrate the
usefulness of the method.
Joint work Yves Dominicy and Hiroaki Ogata
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